Question

cos⁴A-sin⁴ A + 1 = 2 cos²A.
proof​

Answer 1

Answer:

Step-by-step explanation:

LHS=Cos^4A-Sin^4A+1

=(Cos^2A)^2-(Sin^2A)^2+1

={(Cos^2A+Sin^2A)(Cos^2A-Sin^2A)}+1

={1*(cos^2A-sin^2A)+1

=Cos^2A+1-sin^2A

=Cos^2A+Cos^2A

=2Cos^2A

Answer 2

To prove:

cos⁴A - sin⁴A +1=2cos²A

LHS:

cos⁴A - sin⁴A +1

=(cos⁴A - sin⁴A) + 1

Of the form a² - b²=(a+b)(a-b),

=(cos²A+sin²A)(cos²A-sin²A)+1

We know that,

sin²A + cos²A=1

=cos²A-sin²A+1

From sin²A + cos²A=1,

cos²A=1-sin²A................(1)

=(1-sin²A)-sin²A+1

=2-2sin²A

=2(1-sin²A). [Using (1)]

=2cos²A

=RHS

Hence,proved